Protractor-scale



P. J. HARRIMAN PROTRACTOR SCALE.

APPLICATION FILED SI5-PT. 20, 1920.

1,389,946. Pandsept. 6, 1921.

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PAUL JONES l'rAlEtltIALN',v OF AKRON, OHIO.

Specicaton of Letters Patent.

PROTRACTOR-SCALE.

Patented Sept. 6, 1921.

Application led September 20, 1920. Serial No. 411,484.

To all 'whom t mag/ concern VBe it known that I, PAUL J. llAnRliyrAN,

a citizen of the UnitedStates and a resident 'L n n l e of Akron, county of Summit, @tate 9i Ohio, have invented an improvement in `ilrotractor-Scales, of which the following is a specification.

The -form of protractors, which havey usually been employed, consist essentially or" arc-shaped scalesV having graduation lines which radiate from the center o the arc, the more expensive types being provided with a straight edge which swings about the center with its Vedge in a radial position, so that it may be brought into register with the graduations.- While the more accurate Y work may be done, with the latter-type of i structed while the line is protractor, yet it is diliicult to do perfectly accurate work even with this type, as the edge of the instrument cannot be held in exact coincidence with the line to be conbeing drawn with the drawing instrument.

The object of my invention is to provide a protractor scale which may be applied to any plane surface, in a straight line, such as a ruler, T-square, or triangle, and which, when lused in conjunction with a pair of draftsmans dividers, or Compasses, will enable the langle to be laid oil with practically perfect accuracy. Y p

`I accomplish this object by providing a ruler, or similar device, vwith a straight line of an arbitrary length, adapted to be readily spanned ,by an ordinary pair (5f-draftsmans dividers, and which is divided'by a series'l of graduations, consecutively numbered from O to 90, said graduations indicatingdistances from the zero point which are equal to, or V`multiples or" the sines of angles of one-half the number of degrees indicated-.by the numerals of the corresponding graduations, so that a line of a length equal to the distance from the zero point to any particular graduation on the scale will subtend a corresponding number of degreeso'n an arc lhaving as its radius the unit on which the scale isbased,which radius may be .5, or a multiple thereof, which is thesine ,of 300, and is, therefore, indicated on the scale by the distance fromV the zero point to the graduation corresponding to an angle of 60. For a more complete understanding of my invention, reference is made to the accompanying drawing, in which Figure v1 is a plan view of a ruler, or

straight-edge provided with a scale embodying my invention.

F ig. 2 is a diagram illustrating the method of dlaying oil angles by means of the scale, an

Fig. 8 is a geometrical diagram, for demonstration purposes.

As shown in F ig. l a ruler is provided with a straight line or edge which is divided by perpendicularly disposed graduation lines.

ai, said graduations being numbered consecutively i'rom 0 to 90 and suitable numerals being applied to at least every tenth space, although, it will be obvious that the numbering and variations in length of the graduation lines are entirely matters of convenience 1n use, and that the spaces between the graduations which are shown may be subdivided by other graduat-ions. The form shown in the drawing has been found to be an especially convenient arrangement, and subdivisions into tenths enable the ready use of decimals in connection therewith. These spaces, as will be explained, indicate degrees and are thus identified, and, at the o point, a special mark is preferably formed, as the arrow y, which is identified as the constant radius point, and, in practice this radius, from VO to 60 is preferably l decimeter, or l0 centimeters long. That is, the length of the radius is equal to the unit or" the scale, orto a multiple thereof, and indicates the sine of an angle oi' 300, which is .5, or the sine of one-half a 60O angle.A As the metric system may be much more conveniently employed, in thisjconnection, than English measure, the radius constant may be conveniently set at the distance above indicated. Y

The graduations fromA 0 to 900 are accurately laid out in direct proportion to the length of this radius, each distance from 0 to any .degree point on the scale being in direct proportion to the sine of an angle oi one-half the corresponding number of degrees indicated by such point,.so that if a circle having the unitary distance from 0 to 60 as a radius, is inscribed about a right triangle, as A. B. C. in F ig. 3, its hypotenuse A. C. will then coincide with a diameter of the circle, and the length of the shorter side will correspond to a distance on the scale from the Zero point Vto a certain degree point, which will be twice, in denomination, the number of degrees of the angle of the triangle oppositethe shorter side A. B.

As it V`may be proved geometrically that this angle is eXactly onefhalf theangle which would be formed by drawing a line from the vertex of the right angle of the triangle to the center O, of the hypotenuse, which is the center 'of the circle in which the triangle Y Was inscribed, it follows that if the distance Y on the scale for a. certain number of degrees is laid out, as a chord, on an arc having the distance from to 60 as a radius and lines are drawn from the ends of the chord to the center of the arc, an angle Vhaving the same number of degrees will be constructed.

Therefore, as illustrated in Fig. 2, in using` Y the scale, to lay off an angle of a certain number of'degrees from the lineV O, A, which will have its vertex at the point `@,the di- ;the 'dividers on the point A, aV short arc is struck, which intersects, at B, the arc which has been struck from the center O. .Y

Then a line is drawn from points B to. O giving the desired angle A. O. B.

Tov prove that this line A. B. varies clirectly as the sine of 1; the angle which is thus formed, reference is made to Fig. 3, in which tvvoright trianglesA. B. C. and A. BC areV shownas inscribed ina circle having the scale unit 0 to 60", as a radius, and having the sides -A. B. and A. B.- repre-Y sent distances fromptlie.. zei'c point to any;

tWo points on the scale.

l,It may be demonstratedV geometrically I. AOB =.2 ACB, 0r ACB= AOB i Bytrigonometry i i B IV sin@ Aon figg gia Y 'simmer/ Anus AC j Inaccordance Withfproposition 1.,'by sub-V s titution---V Y' V SineLAOB .Y `'lhere-fore, eachdistance from Ythe `zero, Vpoint to any Vone of theV graduations or degree Combining these Vequations in a properV Y Y ,Y straight line, Or ifa series of suitably num- Y bered pointsfwere provldedvvhich Were'arpoints, on the scale, is in direct proportion to the sineV of the angle having one-half the corresponding Vnumber of degrees, indicated by the graduation, each of said distances thus being equal to the chord Which Will subtend thearc which measures an angle having the full number of degrees indicated by the graduation.

If the distance on then the total length of the scale from O to 90 will be 14.14 centimeters, the sine of 60", or 30". being .5 and the sine of 900, 0r

the scale from O tolO Y is 1 decimeter, or 10 centimeters, as shown,

O being :707, as may be ascertained from any table of natural sines. That is, on4 the basis of centimeters, the factor 20 isused to determine the actual line as distanceV in each instance. For example the sine of an angle of 20O vis .342, so that the distance from O to 40 on ascale made up on the above basis would be 6.84 centimeters.

From the foregoing description it Will beV apparent that an angle may beV quickly laid off with perfect accuracy bythe employment ofV a pair of dividers -in Vconjunction with the scale above described, and it Will.` be also apparent that the scale is adapted for application to any plane surface, such as a ruler, T-square, 4or draftmans triangle, Yso that it may be conveniently carried Yabout and employed, and the provision of a separate drafting instrument for the purpose of laying off angleswill beunnecessary.

It Will be understood that, While it is'desirable, as a matterof- Vconvenience and accuracy, that the scale beQactually Vprovided with a straight line, the actualvforrnation of a straight line thereon is not essential, it merely being essential that the graduations be made vvwith relationV to fanv imaginary straight line, so that it Will be understood" that, inV the zclaims, vthe limitation to a straight line is intended to include either an actual or` an imaginary straight line.

It, will also be understood that it VWould'loe possible to secure the same resultsY if the graduations-were laid out/on a curved or an irregular line, provided `the straight; line distance from the zero; point .to each gradua- Y tion thereon were the sam-e as `the corresponding distances Would be if laid 'ont on a ranged at straight line distances from the graduations.V V Howe-ver, the form .of themventionshovvnV ismore workable'and convenient than any. other form of `Which I am aware. Y

I claim:

' 1. A protractor Scale hav-ing a line! divided by consecutively numbered graduations, one Y,

`ofv'vv'hich,indicatesthe.unit on which theV Vscale isbased, and'all ofwhichfindicate straight line distances from the initial point of the line which are each equal to the sine of an angle having a number of degrees corresponding to the numeral of the graduation.

2. A protractor scale having a graduated line, the graduations thereof being consecutively numbered and so arranged that the straight line distances from the zero point to each of said graduations is in direct proportion to the sines of angles of one half the number of degrees indicated by the respective numerals of the graduations, and means on the scale indicating the length of radius of an arc on which said distances may be laid oil as chords, to indicate the position of the sides of the corresponding angles,

3. A protractor scale having a graduated straight line in which the graduations are consecutively numbered from 0 to 9() and in which the distance from the 0 to the 60 point indicates the unit on which the scale is based and the other graduations indicate, on the basis of the unit, distances from the zero point thereto Which are equal to the sines of angles of one-half the number of degrees indicated by the numeral of the corresponding graduation.

4. A protractor scale having a series of consecutively numbered points arranged at straight line distances from an initial point, which are respectively equal to the length of chords Which will subtend arcs of a circle having a radius equal to one of said distances, the number of degrees in each arc thereof being equal to the number of the point indicating the length of its chord.

In testimony whereof I have signed my name to this specification.

PAUL JONES HARRIMAN. 

